Relativistic Euler equations Guide, Meaning , Facts, Information and Description

In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of special relativity.

The equations of motion are contained in the continuity equation of the Stress-energy tensor :

For a fluid, (here is the relativisitic rest energy of the fluid, is the pressure, is the four-velocity of the fluid, and is the metric tensor.

To the above equations, a statement of conservation is usually added, usually conservation of baryon number. If is the number density of baryons this may be stated

These equations reduce to the classical Euler equations if .

The relativistic Euler equations may be applied to calculate the speed of sound in a fluid with a relativisic equation of state (that is, one in which the pressure is comparable with the internal energy density , including the rest energy; where is the classical internal energy).

Under these circumstances, the speed of sound is given by

(note that is the relativisic internal energy density). This formula differs from the classical case in that has been replaced by .

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